"cheap hotel," hobo slang, 1904, probably related to slang flop (v.) "lie down for sleep" (1907); see flop (v.) + house (n.). The explanation below is not found in other early references.

In one of [Cincinnati's] slum districts stands the Silver Moon, a "flop house" (i.e., a house where the occupants are "flopped" out of their hanging bunks by letting down the ropes) .... ["McClure's" magazine, November 1904]